cggglm (3p)

Name

cggglm - Markov linear model (GLM) problem

Synopsis

SUBROUTINE CGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)

COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
INTEGER N, M, P, LDA, LDB, LDWORK, INFO

SUBROUTINE CGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
INFO)

COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO




F95 INTERFACE
SUBROUTINE GGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
LDWORK, INFO)

COMPLEX, DIMENSION(:) :: D, X, Y, WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO

SUBROUTINE GGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
LDWORK, INFO)

COMPLEX, DIMENSION(:) :: D, X, Y, WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO




C INTERFACE
#include <sunperf.h>

void  cggglm(int  n, int m, int p, complex *a, int lda, complex *b, int
ldb, complex *d, complex *x, complex *y, int *info);

void cggglm_64(long n, long m, long p, complex *a,  long  lda,  complex
*b,  long  ldb,  complex  *d,  complex  *x,  complex *y, long
*info);

Description

Oracle Solaris Studio Performance Library                           cggglm(3P)



NAME
       cggglm - solve a general Gauss-Markov linear model (GLM) problem


SYNOPSIS
       SUBROUTINE CGGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
             INFO)

       COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
       INTEGER N, M, P, LDA, LDB, LDWORK, INFO

       SUBROUTINE CGGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK, LDWORK,
             INFO)

       COMPLEX A(LDA,*), B(LDB,*), D(*), X(*), Y(*), WORK(*)
       INTEGER*8 N, M, P, LDA, LDB, LDWORK, INFO




   F95 INTERFACE
       SUBROUTINE GGGLM(N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
              LDWORK, INFO)

       COMPLEX, DIMENSION(:) :: D, X, Y, WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER :: N, M, P, LDA, LDB, LDWORK, INFO

       SUBROUTINE GGGLM_64(N, M, P, A, LDA, B, LDB, D, X, Y, WORK,
              LDWORK, INFO)

       COMPLEX, DIMENSION(:) :: D, X, Y, WORK
       COMPLEX, DIMENSION(:,:) :: A, B
       INTEGER(8) :: N, M, P, LDA, LDB, LDWORK, INFO




   C INTERFACE
       #include <sunperf.h>

       void  cggglm(int  n, int m, int p, complex *a, int lda, complex *b, int
                 ldb, complex *d, complex *x, complex *y, int *info);

       void cggglm_64(long n, long m, long p, complex *a,  long  lda,  complex
                 *b,  long  ldb,  complex  *d,  complex  *x,  complex *y, long
                 *info);



PURPOSE
       cggglm solves a general Gauss-Markov linear model (GLM) problem:

               minimize || y ||_2   subject to   d = A*x + B*y
                   x

       where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given N-
       vector. It is assumed that M <= N <= M+P, and

                  rank(A) = M    and    rank( A B ) = N.

       Under these assumptions, the constrained equation is always consistent,
       and there is a unique solution x and a minimal 2-norm solution y, which
       is obtained using a generalized QR factorization of A and B.

       In  particular, if matrix B is square nonsingular, then the problem GLM
       is equivalent to the following weighted linear least squares problem

                    minimize || inv(B)*(d-A*x) ||_2
                        x

       where inv(B) denotes the inverse of B.


ARGUMENTS
       N (input) The number of rows of the matrices A and B.  N >= 0.


       M (input) The number of columns of the matrix A.  0 <= M <= N.


       P (input) The number of columns of the matrix B.  P >= N-M.


       A (input/output)
                 On entry, the N-by-M matrix A.  On exit, A is destroyed.


       LDA (input)
                 The leading dimension of the array A. LDA >= max(1,N).


       B (input/output)
                 On entry, the N-by-P matrix B.  On exit, B is destroyed.


       LDB (input)
                 The leading dimension of the array B. LDB >= max(1,N).


       D (input/output)
                 On entry, D is the left hand side of the  GLM  equation.   On
                 exit, D is destroyed.


       X (output)
                 On exit, X and Y are the solutions of the GLM problem.


       Y (output)
                 On exit, X and Y are the solutions of the GLM problem.


       WORK (workspace)
                 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.


       LDWORK (input)
                 The dimension of the array WORK. LDWORK >= max(1,N+M+P).  For
                 optimum performance, LDWORK >= M+min(N,P)+max(N,P)*NB,  where
                 NB  is  an upper bound for the optimal blocksizes for CGEQRF,
                 CGERQF, CUNMQR and CUNMRQ.

                 If LDWORK = -1, then a workspace query is assumed;  the  rou-
                 tine  only  calculates  the  optimal  size of the WORK array,
                 returns this value as the first entry of the WORK array,  and
                 no error message related to LDWORK is issued by XERBLA.


       INFO (output)
                 = 0:  successful exit.
                 < 0:  if INFO = -i, the i-th argument had an illegal value.




                                  7 Nov 2015                        cggglm(3P)